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Computer Science > Distributed, Parallel, and Cluster Computing

Title:
Analyzing Distributed Join-Idle-Queue: A Fluid Limit Approach

Abstract: In the context of load balancing, Lu et al. introduced the distributed
Join-Idle-Queue algorithm, where a group of dispatchers distribute jobs to a
cluster of parallel servers. Each dispatcher maintains a queue of idle servers;
when a job arrives to a dispatcher, it sends it to a server on its queue, or to
a random server if the queue is empty. In turn, when a server has no jobs, it
requests to be placed on the idle queue of a randomly chosen dispatcher.
Although this algorithm was shown to be quite effective, the original
asymptotic analysis makes simplifying assumptions that become increasingly
inaccurate as the system load increases. Further, the analysis does not
naturally generalize to interesting variations, such as having a server request
to be placed on the idle queue of a dispatcher before it has completed all
jobs, which can be beneficial under high loads.
We provide a new asymptotic analysis of Join-Idle-Queue systems based on mean
field fluid limit methods, deriving families of differential equations that
describe these systems. Our analysis avoids previous simplifying assumptions,
is empirically more accurate, and generalizes naturally to the variation
described above, as well as other simple variations. Our theoretical and
empirical analyses shed further light on the performance of Join-Idle-Queue,
including potential performance pitfalls under high load.

Comments:

11 pages, draft paper, likely to be at Allerton 2016, possibly improved before then